Re: the competition's expm vs ours

[Jaroslav Hajek]

On Wed, Dec 10, 2008 at 9:23 AM, Marco Caliari <address@hidden> wrote:
>> On  9-Dec-2008, Jaroslav Hajek wrote:
>>
>> I wonder whether there's
>> room to optimize further, but I don't see anything left.
>
> If you allow to precompute another auxiliary matrix
>
> a4 = a2^2;
>
> then you can rewrite
>
> x = (c(8) * a4 + c(6) * a2) * a4 + c(4) * a4 + c(2) * a2 + id;
>
> At this point, you can even increase by one the degree of the approximation
> (at the same cost) and write
>
> y = ((c(9) * a4 + c(7) * a2) * a4 + c(5) * a4 + c(3) * a2 + c(1) * id) * aa;
>
> Of course, you need a new set of coefficients c(1:9).
>

OK, interesting :) I uploaded the new expm code, so feel free to
suggest patches.


> Best regards,
>
> Marco
>



-- 
RNDr. Jaroslav Hajek
computing expert
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz